Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ax-cnre | Unicode version |
Description: A complex number can be expressed in terms of two reals. Definition 10-1.1(v) of [Gleason] p. 130. Axiom for real and complex numbers, justified by theorem axcnre 7689. For naming consistency, use cnre 7762 for new proofs. (New usage is discouraged.) (Contributed by NM, 9-May-1999.) |
Ref | Expression |
---|---|
ax-cnre |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 | |
2 | cc 7618 | . . 3 | |
3 | 1, 2 | wcel 1480 | . 2 |
4 | vx | . . . . . . 7 | |
5 | 4 | cv 1330 | . . . . . 6 |
6 | ci 7622 | . . . . . . 7 | |
7 | vy | . . . . . . . 8 | |
8 | 7 | cv 1330 | . . . . . . 7 |
9 | cmul 7625 | . . . . . . 7 | |
10 | 6, 8, 9 | co 5774 | . . . . . 6 |
11 | caddc 7623 | . . . . . 6 | |
12 | 5, 10, 11 | co 5774 | . . . . 5 |
13 | 1, 12 | wceq 1331 | . . . 4 |
14 | cr 7619 | . . . 4 | |
15 | 13, 7, 14 | wrex 2417 | . . 3 |
16 | 15, 4, 14 | wrex 2417 | . 2 |
17 | 3, 16 | wi 4 | 1 |
Colors of variables: wff set class |
This axiom is referenced by: cnre 7762 |
Copyright terms: Public domain | W3C validator |